A number of devices are commercially available that analyze signals to facilitate the design, manufacturing, and calibration of electronic and communication devices and systems. Examples of signal analyzers include the Agilent Technologies, Inc.'s 89400 and 89600 series vector signal analyzers (VSA). When analyzing signals on a signal analyzer, the measured signal is typically presented in the form of a trace representing the frequency domain output of a Fourier transform calculated from samples of the measured signal. The trace consists of the individual points in the frequency domain. In general, an odd number of points are used so that the center point will lie exactly at the center frequency of the frequency span.
For simple single-tone measurements, if the exact tone frequency is known and the equipment (the signal generator and the analyzer) is locked to a frequency reference source, the user may place the signal on the analyzer center frequency. By doing so, measuring the amplitude of the single-tone signal is relatively straight-forward, because the amplitude may be observed from the marker or trace amplitude at the exact center frequency point in the frequency domain. When measuring multi-tone signals, however, most of the tones do not lie at the center frequency and, generally, do not lie exactly on the frequency domain points of the analyzer trace. Instead, most of the tones will lie between two respective trace points. Accordingly, a simple marker measurement is unsuitable for measuring multi-tone signals. The measurement of any single-tone that does not lie exactly at the analyzer center frequency and the measurement of tone(s) produced by equipment that is not locked to the same frequency as the analyzer present similar complications.
Moreover, the measurement of the accurate amplitude and frequency of each tone of a multi-tone signal where the exact frequencies of the tones are unknown beforehand is quite complicated. In general, two traditional approaches have been used to address this type of signal analysis. The first approach uses a Flattop Fourier window function during the analyzer sweep. In the second approach, a Hanning or other raised-cosine window function is used.
By employing the Flattop Fourier window function, the frequency domain representation of the multi-tone signal is widened or flattened. Typically, the tone peak of the multi-tone signal will be widened and flattened on the trace such that two or three trace points will be generated around each tone peak of the multi-tone signal being analyzed. The peak trace amplitude in this region may be read or marker-to-peak and read steps may be performed to estimate the amplitude of the actual peak within 0.01 dB of the “correct result.” The “correct result” refers to the result that would be obtained if the signal frequency could be placed at exactly one of the analyzer trace points. Also, the accuracy of the measurement is generally independent of the difference in frequency between the tone being measured and the respective two or three trace points adjacent to the tone.
Some frequency information may be gathered from this trace. However, the accuracy of the gathered frequency information is limited by the frequency resolution between the analyzer trace points. The accuracy of the frequency resolution is often less because of the widening effect of the Flattop Fourier window function and the fact that the amplitude of the two or three trace points adjacent to the actual peak typically have magnitudes within approximately 0.01 dB. Moreover, noise effects may also cause the trace point with the peak amplitude to not be the trace point that is closest to the actual peak point. Thus, the Flattop Fourier window causes frequency measurement to be quite difficult. An artificially tight analyzer resolution bandwidth (RBW) may be employed to address the difficulty. However, this may cause the test time to increase and may cause the measurement to become impractical. Another alternative may be employed in which an ordinary RBW is used for most of the trace and a much smaller RBW is used around selected marker positions. However, this requires multiple sweeps. Specifically, at least one sweep is needed to identify the approximate tone frequencies and one sweep is needed for each tone to place the marker near the position of the respective tone to measure its frequency using the smaller RBW.
There is also a performance constraint associated with the use of the Flattop Fourier window function. Specifically, when this window function is used, the number of required analyzer trace points may increase by a factor of 3.82 as compared to the use of a Uniform window function (depending upon the analyzer employed). This factor may dramatically increase the acquisition time of the analyzer. Also, if the signal to be measured has a wide bandwidth and a narrow RBW is desired for signal-to-noise ratio (SNR) reasons, the factor may require the measurement process to be split into multiple subsections of the signal bandwidth to accommodate analyzer limitations.
By employing a Hanning or other raised-cosine window function, the measurement process will execute more quickly, because the number of trace points is only increased by a factor of 1.5 as compared to a Uniform window function. Moreover, the signal peaks exhibited by the analyzer trace are significantly more sharp than exhibited by the Uniform window function. However, amplitude accuracy may be lost. If a tone of the signal being measured lies almost exactly between two analyzer trace points, the peak amplitude value read from one of the trace peaks may deviate by 1.4 dB from the actual amplitude. This deviation is greatest when the RBW is selected to equal the minimum allowed for a given number of trace points. Clearly, this amount of potential deviation is unsuitable if accurate amplitude measurements are necessary for a particular application.